Question

jane drives 81km west, then 25km south, then 15km east and finally 30km south in 4 hours. find her displacement. displacement: 85.9km @ 39.8 degrees s of w..... does anyone know how to work out this problem???

Answer 1

You could just draw the problem (scaled of course) and work it out from there....

You could also represent each trip with a vector and use vector operations to find the final point on the map. Knowing that "sides" of the earth go like:
N
W E
S
you can spot the resemblance with the standard coordinate system:
^y
|
___|____>x
|
|
and say that
\[leg_1 = -81\hat x
\\leg_2 = -25\hat y
\\leg_3 = 15\hat x
\\leg_4 = -30\hat y\]
after which you just have to add the legs together as vectors, if you're more comfortable the alternative (more accepted method of labeling the vectors) is if you use the standard i, j and k letters for unit vectors.